Embed Size (px)
Citation preview
N A S A C O N T R A C T O R
R E P O R T
N A S A C R - 2 4 1 2
CSi
•<uo•<
TESTING TECHNIQUES FOR DETERMINING
STATIC MECHANICAL PROPERTIES
OF PNEUMATIC TIRES
by R. N. Dodge, R. B. Larson, S. K. Clark,
and G. H. Nybakken
Prepared by
THE UNIVERSITY OF MICHIGAN
Ann Arbor, Mich. 48105
for Langley Research Center
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • JUNE 1974
https://ntrs.nasa.gov/search.jsp?R=19740017443 2020-03-19T08:30:03+00:00Z
1. Report No. 2. Government Accession No.
NASA CE-2412
4. Title and SubtitleTESTING TECHNIQUES FOR DETERMINING STATIC MECHANICAL PROPERTIESOF PNEUMATIC TIRES
7. Author(s)
R. N. Dodge, R. B. Larson, S. K. Clark, and G. H. Nybakken
9. Performing Organization Name and Address
The University of MichiganAnn Arbor, Michigan U8105
12. Sponsoring Agency Name and Address
National Aeronautics and Space AdministrationWashington, B.C. 205^6
3. Recipient's Catalog No.
5. Report DateJune 197!)-
6. Performing Organization Code
8. Performing Organization Report No.
056080- 20-T
10. Work Unit No.
501-38-12-02
11. Contract or Grant No.
NGL- 23-00 5-010
13. Type of Report and Period Covered
Contractor Report
14. Sponsoring Agency Code
15. Supplementary Notes
Topical report.
16. Abstract
Fore-aft, lateral, and vertical spring rates of model and full-scale pneumatic tires
•were evaluated by testing techniques generally employed by industry and various testing
groups. The purpose of this experimental program was to investigate what effects the
different testing techniques have on the measured values of these important static tire
mechanical properties. The testing techniques included both incremental and continuous
loadings applied at various rates over half, full, and repeated cycles.
Of the three properties evaluated, the fore-aft stiffness was demonstrated to be the
most affected by the different testing techniques used to obtain it. Appreciable differ-
ences in the fore-aft spring rates occurred using both the increment- and continuous-loading
techniques; however, the most significant effect was attributed to variations in the size of
the fore-aft force loop. The dependence of lateral stiffness values on testing techniques
followed the7;Vamejtrends .as that for fore-aft stiffness, except to a lesser degree. Vertical
stiffness values were found to be nearly independent of testing procedures if the nonlinear
portion of the vertical force-deflection curves is avoided.
17. Key Words (Suggested by Author(s))
Aircraft tires
Tire mechanical properties
Tire testing techniques
19. Security Classif. (of this report)
Unclassified
18. Distribution Statement
Unclassified - Unlimited
STAR Category 02
20. Security Classif. (of this page) 21. No. of Pages 22. Price*
Unclassified W $3.25
For sale by the National Technical Information Service, Springfield, Virginia 22151
TABLE OF CONTENTS
Page
SUMMARY !
INTRODUCTION 2
SYMBOLS ^
TEST PROCEDURES AND RESULTS 5
CONCLUDING REMARKS ,,„
111
LIST OF ILLUSTRATIONS
Table Page
I. Tire Descriptions 10
II. Tire Operating Conditions 11
III. Summary of Static Fore-Aft Stiffness, k (ib/in.) - 15X
IV. Summary of Static Lateral Stiffness, k (ib/in.) 29<y
V. Summary of Static Vertical Stiffness, k (ib/in.) 38z
Figure
1. Tire coordinate directions. 5
2. Photograph of fore-aft test'apparatus for model tires. . 7
J. Photograph of fore-aft test apparatus for full size tires. 8
k. Typical fore-aft, increment load, force-deflection plots formodel and full size tires. 17
5. Fore-aft force-deflection loops illustrating effect of loopsize for a model tire. . 19
6. Fore-aft force-deflection loops illustrating effect of loopsize for a full size tire. 20
7« Dimensionless plot of fore-aft stiffness versus loop size forall tires. 23
8- Fore-aft force-deflection loop illustrating tire slippageduring testing of a model tire. 2k
9- Fore-aft force-deflection loop illustrating small, unidirec-tional slippage during testing of a model tire. 2U
10. Lateral force-deflection loop illustrating dog leg type loopgenerated during testing of a full size tire. 25
11. Photograph of lateral test apparatus for model tires. 28
iv
LIST OF ILLUSTRATIONS (Concluded)
Figure Page
12. Photograph of lateral test apparatus for full size tires. 28
13- Typical lateral, increment load, force-deflection plots formodel and full size tires. 31
14. Lateral force-deflection loops illustrating effect of loopsize for a model tire. 33
~1"5 Late ral~f or c'e de flee tron—loops—rllus tr at ing-e f f e c t—o f—lo opsize for a full size tire. 3)4.
16. Dimensionless plot of lateral stiffness versus loop size forall tires. 35
17- Photograph of vertical test apparatus for model tires. 35
18« Typical vertical force-deflection loop for a model tire. 30
19. Typical vertical force-deflection loop for a full size tire.
TESTING TECHNIQUES FOR DETERMININGSTATIC MECHANICAL PROPERTIES OF PNEUMATIC TIRES
By R. N. Dodge, R. B. Larson, S. K. Clar.k, and G. H. Nybakken
SUMMARY
Fore-aft, lateral, and vertical spring rates of model and full-scale
pneumatic tires were evaluated by testing techniques generally employed
by industry and various testing groups. The purpose of this experimental
program was to investigate what effects the different testing techniques
have on the measured values of these important static tire mechanical
properties. The testing techniques included both incremental and contin-
uous loadings applied at various rates over half, full, and repeated cycles.
Of the three properties evaluated, the fore-aft stiffness was demon-
strated to be the most affected by the different testing techniques used
to obtain it. Appreciable differences in the fore-aft spring rates
occurred using both the increment- and continuous-loading techniques; how-
ever, the most significant effect was attributed to variations in the size
of the fore-aft force loop. The dependence of lateral stiffness values on
testing techniques followed the same trends as that for fore-aft stiffness,
except to a lesser degree. Vertical stiffness values were found to be
nearly independent of testing procedures if the nonlinear portion of the
vertical force-deflection curves is avoided.
INTRODUCTION
Engineers measure and evaluate static mechanical properties of pneumatic
tires for various reasons. Often the numerical values of these properties are
exchanged among many engineering groups. This flow is an admirable exchange
of technical knowledge and an economic use of time and effort. However, the
indiscriminant use of such information can be unwise if these numerical values
are not measured and interpreted consistently from one source to another. Thus,
there is a definite need to investigate the effects of testing procedures and
techniques on the static mechanical properties of pneumatic tires. Also, if
it is evident that some properties are highly susceptible to testing techniques,
it is possible that guidelines could be established for such measurements.
The general purpose of the test program.discussed here was to systemat-
ically investigate the effects of testing techniques on three important statics
mechanical.properties of pneumatic tires. These effects were to be studied on
both scaled model aircraft tires as well as full size tires. In addition, it
was hoped that this work would be useful in establishing criteria for measuring
those properties that are highly influenced by testing techniques.
The static mechanical properties cnosen for this study were vertical, lat-.
eral, and fore-aft spring rates. Each of these properties was to be measured
and evaluated-by various techniques and their results compared with one another.
The techniques were to be varied according to the numerous methods.used in the
past by various testing groups.
The research group concerned with this program has been actively involved
in establishing structural modeling laws of pneumatic tires [!]• Some validity
has been established for these laws by showing favorable correlation between
some mechanical properties of prototype and model aircraft tires constructed
according to the modeling laws. These model aircraft tires are used in this
investigation as well as a variety of full size automobile and aircraft tires.
SYMBOLS
English Letters
D - tire diameter
F - tire fore-aft forcex
F - maximum tire fore-aft forcexm
F - tire lateral forceyF - maximum tire lateral force
F - tire vertical forcez
F - maximum tire vertical forcezm
k - tire fore-aft elastic stiffnessx
k - tire lateral elastic stiffnessyk - tire vertical elastic stiffnessz
p - tire inflation pressureo
x,y,z - tire coordinate directions (see Figure l)
Greek Letters
8 - tire fore-aft deflectionx
5 - maximum tire fore-aft deflectionxm
6 - tire lateral deflectiony8 - maximum tire lateral deflectionym
8 - tire vertical deflectionz
8 - maximum tire vertical deflectionzm
TEST PROCEDURES AND RESULTS
The two coordinate system used in this work is shown in Figure 1. The
mechanical properties discussed are described in terms of these coordinates.
The x-direction is referred to as the fore-aft direction, the y-direction as
the lateral direction, and the z-direction as tne vertical direction.
(Vertical)
Figure 1. Tire coordinate directions..
The stiffnesses or spring rates in these directions are defined in terms
of the ratio of applied force to resulting deflection. The fore-aft stiffness
k is defined in terms of the fore-aft load F and the corresponding deflectionX X
5 obtained when a stationary time is first inflated and loaded vertically andX
then subjected to a varying fore-aft load. The lateral stiffness k is definedt/
in terms of the lateral load F and the corresponding deflection 6 obtainedy y
when a stationary tire is first inflated and loaded vertically and then sub-
jected to a varying lateral load. The vertical stiffness k is defined inz
terras of the vertical load F and the corresponding deflection 6 obtainedz z
after a stationary tire is first inflated and then subjected to a varying ver-
tical load.
Data necessary to investigate these properties were collected for both
model and full size tires. The model aircraft tires were built according to
.the modeling laws and procedures discussed by Clark, Dodge, Lackey, and Nybakken
[1]. The model tires used in these tests were scaled from kOx 12-lU PR Type VII
and U9x 17-26 PR Type VII aircraft tires. The full size tires ranged from a
foreign made 155 mm x 15 radial passenger car tire to a 2^ x 7-7-10 PR Type VII
aircraft tire.
Fore-Aft Stiffness
The test apparatus used to obtain fore-aft data for the model tires is
shown in Figure 2. This apparatus is a revision of the Static Testing Device
described in [1]. Its basic structure consists of a tire holding yoke attached
to a counterweighted 90-degree elbow arm which in. turn is attached to a fixed
base through a steel pointed hinge. The yoke assembly is loaded vertically
with dead weights, causing the tire to bear against a movable steel bearing
plate. This plate is supported by three barll bearings rolling in steel guides.
The bearing plate has a high friction surface bonded to it to minimize tire
slippage. The tire was positively locked in the yoke assembly to minimize
'6
JAHM| M||^ ^J[[|
H ^ ^ ^ BHWP r -
s\
Figure 2. Photograph of fore-aft test apparatus for model tires.
wheel windup during the fore-aft tests. The three ball bearing supports had
low friction characteristics and the effective friction coefficient of the
total apparatus was 0.0158- This friction coefficient also held for tne lat-
eral tests.
Fore-aft data for the model tires were generally obtained by inflating
the tire to a prescribed internal pressure and loading the tire vertically with
a prescribed load. A varying fore-aft load was applied to the bearing plate
through the screw assembly. Force was monitored by a calibrated force trans-
ducer located between the screw assembly and the bearing plate. Displacement
was monitored by a Linear Variable Differential Transformer located between the
yoke and the bearing plate. The placement of the LVDT is important, especially
in fore-aft stiffness tests where the spring rate of the tire is high. The
spring rate of the tire in tne fore-aft direction can easily be of tne same
7
order as the support structure. Measurement of the true tire deflection re-
quires the relative displacement of the wheel hub and the bearing plate. Be-
cause of the positive locking procedures used in these tests, wheel windup was
found to be negligible. Thus, the relative displacement between the wheel yoke
and the bearing plate was used as the measure of tire deflection. The output
signals of both transducers were amplified through carrier preamplifiers and
recorded on a x-y plotter to give a force-deflection record.
The test apparatus used to obtain fore-aft stiffness data for the full
size tires is shown in Figure J. The apparatus is a modification of a Riehle
Figure J. Photograph of fore-aft test apparatus for full size tires.
Tensile Test Machine into a slow-rolling flat plank machine. The wheel is
bolted to the axle, which is rigidly bolted to the yoke which is bolted to the
loading head of the testing machine. The tire is loaded vertically through
8
the loading mechanism of the machine, causing the tire to bear against a mov-
able flat plank. The top surface of the plank directly under the tire has a
number 80 grit sanding belt bonded to it. The plank is supported by low fric-
tion rollers located directly under the loading area and is guided by ball
bearings located along the length of the plank and running against a stationary
steel angle guide. This plank arrangement results in low friction character-
istics and has an effective friction coefficient of 0.006, considerably lower
than the model tire system. The fore-aft load is applied to the end of the
movable plank. A tension-compression load cell is placed between the loading
screw and the plank. The displacement is measured with the same LVDT used in
the model tests. Again the LVDT is located between the plank and the yoke,
since wheel-axle windup was negligible with the rigid system used in these
tests.
The fore-aft data for the full size tires were obtained in the same manner
as the data for the model tires. One minor difference was caused by the nature
of the two loading systems. The model tires were always operating under a
fixed vertical load while the full size tires were always operating under fixed
vertical deflection. However, the basic operation of the full size test appa-
ratus was very similar to that used for the model tires.\
A brief description of the model and full size tires used in these tests
is given in Table I. The A-series model tires are scale models of U0xl2-li* PR
Type VII aircraft tires with a scale factor of 8-65 and the B-series model
tires are scale models of k9x 17-26 PR Type VII aircraft tires with a scale
factor of 12. Each model tire had been run through a break-in period before
9
TABLE I
TIRE DESCRIPTIONS
Model Tires
A24
A2JP
B21
B23
B26
B291
Full Size Tires
12
345678910
10M
2-ply bias model of 40 xcrown angle 39°, 840/2
2-ply bias model of 40 xcrown angle 36°, 840/2
2-ply bias model of 1*9 xcrown angle 42°, 840/2
2-ply bias model of 49 xcrown angle 42°, 840/2
2-ply bias model of 49 *crown angle 4l°, 840/2
2-ply bias model of 49 xcrown angle 34°, 840/2
12-14 PR Type VII,Nylon, 10 EPI12-14 PR Type VII,Nylon, 10 EPI
17-26 PR Type VII,
Nylon, 28 EPI
17-26 PR Type VII,Nylon, 28 EPI
17-26 PR Type VII,Nylon, 10' EPI
17-26 PR Type VII,Nylon, 10 EPI
24 x 7-7-10 PR Type VII, aircraft8.00 x 14, 4-ply bias, automobile7.50 x 14, 2-ply bias, automobile7.50 x .14, 4-ply radial, foreign, automobile5.90 x 15, 4-ply bias, foreign, automobile
155 x 15, radial, foreign, automobile215 R 15, radial, automobile7.50 x 14-8 PR Type III, aircraftH78-15, belted bias, automobileG78-15> belted bias, smooth tread, automobile
G78-15> belted bias, smooth tread, automobile
being used in any test. Most of the full size tires had not gone through such
a break-in period.
The operating conditions for the model and full size tires are given in
Table II. For the model tires, the vertical force is prescribed while the ver-
tical deflection is prescribed for the full size tires. The full size tire
vertical deflections were obtained by loading the tires to the approximate
rated load as specified by the Tire and Rirn Association and then measuring the
10
TABLE II
TIRE OPERATING CONDITIONS
Tire
A24A23PB21B2JB26B2912
34567891010M
D(in.)
4.554.554.oo4.004.004.00
23.725.127-926.9 '25-824.528.2
27.528.427.727.7
PO(psi)
2020
2525252585242424202024872424"24
Fz(Ib)
41.641.631.631.631.631.64800*1175*1085*1085*770*770*1510*5400*1510*1380*1380*
bz(in.)
• 327*.319*.211*.216*.224*.197*1.901.1251.001.341.001.251.751.701.241.001.00
Fxm(lb)
± 6± 6± 6± 6± 6± 6
—±225±275±250±200
±175±300±500±300±250±250
Fym(lb)
± 5± 5± 5± 5± 6± 5
—±200
±225±200±150±150±250±500±250±230±230
*Approximate values.
deflections. Also shown in Table II are the maximum and minimum fore-aft load
F and lateral load F used for most of the tests,xm ym
Eight different testing techniques were used to obtain fore-aft stiffness
data. Each of these techniques is described below by number and the results
from their use are discussed. All of the tires listed in Tables I and II were
not subjected to all eight testing techniques. For tests i-7, the model tires
were run on number 220 grit silicon carbide sandpaper and the full size tires
were run on number 80 grit sanding belt.
Test 1 - Increment loads, half cycle, slow loop.
The tire was pressurized and vertically loaded to the conditions given in
11
Table II. An increment of fore-aft load was applied to the system and held
constant for one minute, at which time the resulting fore-aft deflection was
recorded. The fore-aft load was then increased by the same increment and the
procedure repeated. This incremental loading was continued until the fore-aft
load had reached the maximum F given in Table II. The fore-aft loads werexm
then decreased in a similar manner until the fore-aft load returned to zero.
The resulting force-deflection data were plotted and the fore-aft stiffness kX
determined by averaging the best straight line fits to the increasing and de-
creasing portions of the plots. These best fit straight lines were obtained.
"by eye." The fore-aft stiffness k was also determined .by forming the ratioX
of the maximum fore-aft load F and its resulting deflection 5 to obtainxm , xm
(F /S ). The waiting time of one minute between increments "of load was. axm' xm . •
controlled attempt to allow the £ire to reach equilibrium before recording the
'i ' • .deflection. This test procedure, Test 1, is representative of those used by
testing groups that only have the facilities for taking half-cycle, increment
load data.
Test 2 - Increment loads, full cycle, slow loop.
This test procedure was identical to Test 1 except the load cycle was con-
tinued ' in both directions, thus generating a full cycle of fore-aft load-
deflection data. The fore-aft spring constant k was determined by measuringX
the slope of the line joining the end points of the fore-deflection loop. This
determination of k eliminates the observer's "eye" approximation used in Test 1.X
Again the maximum and minimum fore-aft forces are those given in Table II.
12
Test 3 - Increment loads, full cycle, fast loop.
This test was a repeat of Test 2 except the loads were held constant for
15 seconds instead of one minute. This procedure was a controlled attempt to
determine time effects on increment load tests.
Test k - Continuous loads, slow loop.
This test was also a repeat of Test 2 except the loads were continuously
applied from zero to the maximum F , back through zero to the minimum F andxm xm
back to zero. However, the test was not stopped after one cycle, but continued
for several loops. In these tests, the loops were continued until the gener-
ated loop "homed in" on a single path. In most cases the single path was gen-
erated on the second or third cycle. The time for one complete cycle was ap-
proximately one minute. The value of the fore-aft stiffness k was again de-jC
termined by measuring the slope on the line joining the end points of the force-
deflection loop. This test procedure, Test k, is representative of those test-
ing groups that have the capabilities of obtaining a full loop of force-
deflection through a continuous loading system.
Test 5 - Continuous loads, fast loop.
This test was identical to Test k except the load cycle was completed in
approximately 10 seconds instead of one minute. This test was included to de-
termine time effects for continuous loading conditions.
Test 6 - Continuous loads, slow loop,__ plate deflection.
This test was also identical to Test k except deflections were measured
between the fixed base and the bearing plate. This test was included to illus-
trate possible errors when the wheel, yoke and support mechanism are assumed
rigid.
13
Test 7 - Continuous loads, varying force loop size.
This test was basically the same as Test k with a complete loop generated
in approximately 20 seconds. In this test, the maximum fore-aft force applied
F was varied over a range of values. This procedure resulted in h or 5 dif-xm
ferent size force-deflection loops. The fore-aft stiffness k was determinedA
using the Test 4 procedure of connecting the end points.
Test 8 - Continuous loads, varying contact surface conditions.
This test was also basically the same as Test k. The high friction sur-
face test was the same as in Test U. After this test the tire was thoroughly
cleaned. The high friction surface was removed from the bearing plate and the
metal surface of the plate was cleaned thoroughly. The test procedure described
in Test k was then repeated. Next an oiled surface and then a dirty surface
(oil mixed with grit and sand) were tested in the same manner. Finally, the
plate and tire were thoroughly cleaned and the tire bonded to the bearing plate
with methyl-2 cyanoacrylate. At the instant of bonding, the tire was maintained
at the prescribed operating conditions given in Table II. The test procedure
was then repeated, again using the force loop size given in Table II. Due to
the possibility of tire damage during the unbending, the tires used in this
test, Test 8, were different than the tires used previously in Tests 1-7.
The results of Tests 1-8 are summarized in Table III. The friction forces
of the testing apparatus have not been taken into account in arriving at the
fore-aft stiffnesses given in this table. The results given in the table indi-
cate that all tires, both model and full size, have the same general trends.
However, the different in stiffness values between Test 5 and the preceding
14
CO .COwH
HHCO
M - - PJ •H 05 c
0 -H
ij io"
§ H d-H EH X
EHCO
fc.: O
CO
CO
VO
„
-
HOJ
rH
-UCOQJEH
//
Bo
nd
ed
+ -PrH "7^
•H fto °
rH-Ho
C rH
oJ 03QJ -p•H 0)0 S
Hig
hF
riction
o>eg•HCO X
o o
: F
orc
eV
alu
e
**
^
**
**x
III
/to
/£EH
l J- l VO i i1 CO 1 VQ l P1 KN 1 ^ I l
1 IT\ P t— 1 1
1 KN i KN p p
P P P 1 1 1P P P 1 1 11 1 1 1 1 1
l CO P ON t tl 01 l ^r i l
i VQ t iTN p lI OJ l MD P P
O ITN OON O KN O ONrH ITS 1 rH VQ 1 i— I K N . r H . - d -
+1 +1 +1 +1
COCO COlTN CO J- CO KN.VO 1 ON P -=t t--KN 1 X"N 1 KN KN
+1 +1 +1 +1
^O C — VO O iJ -3" VD KN£>- P OJ P VD ONKN p J- p KN KN
1 l+1 +1 +1 +1
J - O J -3- rH J - J - J - O J
O 1 J- 1 CO rH
"^ 1 J 1
IT\ l O 1 • OJ UN- J- 1 IPi 1 J" -H;
£>- I P I i i-J- 1 1 1 1 TOJ 1 1 1 1 1
rH P KN i KN cOCO 1 rH 1 \X> COKN 1 -3" 1 KN KN
\D l VQ l rH COt— 1 ON 1 lT\ f—
CO l O i O OJ-3- i t-- i j- vbKN. 1 KN. | KA to,
VO 1 £"•*- 1 C — ^J- 1 KN p rH- KN
-3- r J- i oj ro,ITN t. IT\ 1 J- _ _3-
ON 1 O 1 O \£)rH 1 OJ 1 O OJKN 1 KS i KN rO
PM_J- K\ H K> \T) ONOJ OJ OJ OJ OJ OJ< < cq - pq pq pq
P l i l l l P l l O1 1 1 1 1 1 1 1 1 \0P l P i P P l p l O
IT\
1 1 l 1 1 1 1 1 1 O1 1 1 1 1 P 1 1 1 KN1 1 1 1 1 1 1 1 1 t-~
I 1 1 1 P 1 p l 1 O1 1 1 1 1 1 1 1 1 rH1 1 1 1 1 1 P 1 1 ON
1 1 P 1 1 P 1 1 1 O1 1 1 1 1 1 1 P P KNl i i l l l p p p ON
P P I I I I I i i Ot 1 1 1 1 1 1 1 1 v£>1 P 1 P 1 1 1 1 1 ON
L T N O O O O O O O O O O O O OO J v O U \ ^ £ > l T \ ^ J - I 1 O K N O r H O O J l T N C O PO J r H O J v D O J c O l 1 K N M D l A C O K N O N O J J - 1
-J- KN rH I 1 rH VO KN _J- 1-H +1 +1 +1 +1 +1 +1
O O O O O O O O IT\O O O O O O O O OOOJ OO O[>- OKN C— \Q OON O K " N OrH OOJ 1o jo j o jco ojco o j c — rHirS oj\n J-ON G J O J O J L T N I+i -H +1 +i +i' +i -H -fi +i
O O O O O O O O O O O O O O O O O OLTN [••— LTN O ITN VO LT\ C — iTN VO LP\ t~— O CO ^N CO l N ON PrH-H: r H r H rHJ" rHO r H U N rH!>- KNITS rH^J- r-H^D P
8 O O O O O O O O O Q O Q O O OQ O ^ O O O J O i T N O l T S O O J O l T N O O 1 1
LTN J - H O J 5 rH H C- ' " ' -? 1 i 1
O O O O O O O O * O O O O O O O O O OLTNON ITSJ- LTNOJ 1TNO ITSOJ LT\VO OO LTSKN. ITN\£) 1
rH ON O- rH t - - r H H K N ON OJlv D - ^ - O J l T N r — 1 O J O N l T \ l T \ l
O 1 l l l l 1 l P 1KN 1 | p p p 1 1 . 1 1ITS 1 1 1 1 1 1 P 1 P
O O O O O O O O O l. ^ J - ' ^ D r H C T \ \ Q K N O l T N I > - lr H 1 ^ C O C " - l T \ v £ ) C O O N i - H lJ - K N r H K N r H r H ^ D K N ^ t -
O O O O O O O O O lC - J- CO ON KN KN. t — OJ KN 1KN -J- f1— "<O U^ -O \O CO rH 1
O O O O O O O O O lJ - - 4 ~ C O O C - - i r N O N r H Q 1
O O J [ > - K " s j " I T N — { \ Q O lK N K N H K N r H i — 1 v O K N J -
O O O O O O O O O lcO J- ON KN i — I vO \o vO CO iC O O - \ O r H J - J - c o - J - O A iOJ KN r H ' K N (— I rH ITS KN KN.
O O O O O O Q O O lS C O I T N 0 0 - r H O J . O O J K N l
r ^ t ^ - \ O J - ' f ^ C ^ - ' C ^ - O N IO J K N r H O J r H r H i r N K N . K N
O O O O O O O O O lO J O N C O O J C O O H r H t - - l\ O O N \ O O K N J - O J j - i — t 1O J O J r H K A r H . r H i T N t A j -
O J K N . J - I T N \ O C ^ - C O O N O OrH rH
15
four tests is somewhat greater for Tire 2 than any other tire.
A number of specific observations can be made concerning the fore-aft
stiffness tests:
(a) The values of k determined from increment load tests, with the ex-A
ception of Tire 2, ranged from 5-15$, lower than those determined from continu-
ous load tests. See the results for Tests 1-5-
(b) The values of k determined from full cycle increment load data from.A.
model tires were 2-7$> less than those determined from half cycle increment
load data. On the other hand, the full cycle values for the full size tires
ranged from ± 10$, of the half cycle values. A further indication of the dif-
ferences encountered in determining k from half cycle and full cycle incrementJ\
data is shown in Figure k. This figure presents typical increment load force-
deflection plots for a model tire and a full size tire. The friction force is
indicated by the bar in the figure, but has not been subtracted from the data
presented. It is apparent from these plots that the various interpretations
of k mentioned previously can lead to different values of k .x x
(c) The slope of the line from the origin to the maximum force-deflection
point. F /§ , was usually lower than either of the values of k determined' xm7 xnr J x
from the increment load techniques on Tests 1 or 2.
(d) The values of k determined from the fast increment loading loopsX.
were 0-9$, higher than those determined from the slower increment loading loops.
See the results of Tests 2 and 5.
(e) The values of k determined from the faster continuous loading loops,J\
with the exception of Tire 2, were 0-6ffa higher than those determined from the
16
A24P0= 20 psiFz - 41 Ibs.
Fv(lbs.)
T I R E S7.50x 14 TypelHPo = 87 psi
6Z = 1.70 in.
Fx(lbs.)
-0.10 0.08 0.10 6x( in.)
-500-1-
Figure k. Typical fore-aft, increment load, force-deflectionplots for model and full size tires.
17
slower continuous loading loops. See the results of Tests k.and 5-
(f) The values of k determined by measuring the plate deflection andA
assuming it to be equal to the tire deflection were 25- 0$ lower than those
obtained using the relative displacement between yoke and plate. See the re-
sults of Tests 5 and 6. This result is a clear indication of the role of yoke
and support deflections in measuring the relatively stiff fore-aft spring rate
of a tire.
(g) The values of k decreased from 12-50$ as the force loop size was in-.X
creased from a small value to a maximum value. See the results of Test 7- A
further indication of this significant difference is clearly illustrated in
Figures 5 and 6. Figure 5 shows a typical composite force-deflection plot for
two different loop sizes for a model tire. Figure 6 shows the same type of
plot for a full size tire. Again the friction force is indicated on the two
figures, but is not subtracted from the data shown.
(h) The values of k varied less than 5$ for the tests conducted underX
various surface conditions. However, when the model tires were bonded to the
surface, the value of k increased 16-25$, while the full size tire value in-
creased only 5$« It is n°t clearly understood why the increase is so different
between the model tires and the full size tire. The reason may be in the dif-
ference between the contact patch geometries. The model tire has a typical
aircraft tire geometry, with circumferential grooves and little rubber buildup
at the tire shoulders. When loaded to 30-35$ vertical deflection, the tire
has a rounded contact patch [1]. The full size tire is a typical automotive
tire with pronounced shoulders but with no tread pattern. The resulting
18
A24P0
= 20 Psi
Fz=41.6 Ibs.
Fx(lbs.)
10.0 -r
7.5 --
5.0 --
FrictionForce 2.5 --
Fx « ± 10 Ibs.
^ ± 4 Ibs.
-0.0250 -0.0125 7 0.0125 0.0250 6 x ( i n . )
-5.0 --
-7.5 --
-10.0 -L
Figure 5. Fore-aft force-deflection loops illustrating effectof loop size for a model tire.
19
TIRE 87.50 x 14 Type inPo = 87 psi6Z =1.70 in.
Fx( lbs.)
FrictionFx ^ ± 500
0.100 6x(in.)
Figure 6. Fore-aft force-deflection loops illustrating effectof loop size for a full size tire.
20
contact patch is almost a perfect rectangle. These contact patch geometry dif-
ferences may cause different deformation patterns when the tire is bonded to
the plate and distorted in the fore-aft direction. The fact that the fore-aft
stiffness does increase with bonding may have two possible explanations. The
first possible reason may be based on the restraining of the tire contact
patch from stretching- when the tire is bonded. The net deflection for a given
load is less, resulting in a higher spring rate. The second reason is based
on the restraining of local slip in those regions of the contact patch where
the vertical pressure distribution is small. This restriction on the bonded
tire again results in a smaller deflection and a higher spring rate.
From the results and observations discussed above, it seems there are sev-
eral important suggestions to be made in regards to obtaining and interpreting
/
static-fore-aft mechanical properties of pneumatic.tires. First, if. k is mea-X
sured by loading a locked tire against a movable plate which in turn is loaded
in the fore-aft direction, care should be taken to measure relative deflection
between the plate and-the wheel and not between the ground and the plate. Even
using apparatus that appears to be fairly rigid can lead to substantial errors
in deflection measurement, as the results of Test 6 illustrate.
Secondly, a crude estimate of a tire's fore-aft stiffness can be obtained
by applying a single fore-aft 'load and measuring the resulting deflection. The
ratio of these two values gives a reasonable estimate for k .. In general, this.X
estimate will be less than the true value.
Finally, it might be recommended that the most consistent and useful
method for measuring k is with a system that allows full cycle, continuousjC
21
load loops to be generated and recorded in the form of x-y plots. There are
several reasons for this recommendation. First, a consistent interpretation
of the value for k is possible if a full force-deflection loop is available.
This interpretation specifically defines k as the slope of the line joiningj\
the end points of the loop. This method eliminates the need for best fits or
other approximations. However, as the discussion above indicates, a value of
k can only be used and interpreted in a consistent manner if the operatingX
conditions for which the value was measured are well monitored and clearly in-
dicated. In particular, the inflation pressure, the vertical load, and the
fore-aft load loop size should be clearly defined. The inflation pressure and
vertical load can be fixed in relation to an easily obtainable rated condition.
However, no such specification exists for the fore-aft loop size. The effect
of fore-aft loop size on the measured value of the fore-aft stiffness can be
clearly seen in Figure 7- Figure 7 is a composite plot of k as a function ofJ\
varying force loop size in dimensionless form for all the tires tested in Test
7- The results shown in Figure 7 indicate the size of the fore-aft loading
loop must be taken into account when comparing fore-aft stiffnesses of differ-
ent tires. A standard loop size might be defined as a fixed percentage of the
vertical load or the vertical deflection.
The continuous loading full loop also has the advantage of displaying un-
usual and, usually, unwanted characteristics of the load-deflection data. Fig-
ures 8, 9} and 10 are examples of force-deflection loops with undesirable fea-
tures. Figure 8 shows a fore-aft force-deflection loop where slippage has oc-
curred between tire and plate. Comparing Figure 8 with the usual loops in
22
10
+ YRadialsC7 _-/
Aircraft (Type HI
Models
0.01 0.02 0.03 0.04 0.05FX/P0D
2
Figure ?. Dimensionless plot of fore-aft stiffnessversus loop size for all tires.
23
Fx(lbs.)
-0.0250 -0.0125
Figure 8- Fore-aft force-deflection loop illustratingtire slippage during testing of a model tire.
Fx( lbs.)
-0.0250 -0, 0.0250 0.0375 6 x ( i n .
Figure 9. Fore-aft force-deflection loop illustrating small,unidirectional slippage during testing of a model tire.
24
Fy (IbS.)
200-r
100 --
-0.250 -0.125
-100 - -
-200-1-
0.125 0.250 6 (in.)
Figure 10. Lateral force-deflection loop illustrating dog leg typeloop generated during testing of a full size tire.
25
Figure 5 and 6 illustrates the large flat portions at the high loads where
large deflections are occurring with no increase in load. Also, the absence
of a homing in on a single loop indicates that more slippage has occurred in
one direction than the other. Figure 9 illustrates this same effect, even
though the slippage is not obvious. In this case, the lack of a homing in on
a single path is caused by improper locking of the wheel in the yoke. Even
though the force continues to rise with deflection, a slight slippage has oc-
curred between the axle and the yoke. This slippage is unidirectional and re-
sults in the absence of a final, single loop. Figure 10 illustrates a dog-leg
type feature of a force-deflection loop. In this case, the dog leg was gener-
ated by running the plate into an unnoticed obstruction. The obstruction acted
like a stiff spring in series with tire at one end of the loop and caused the
stiffer portion of the loop. Dog-leg loops can also be caused by measuring
the deflection with respect to ground and having a support structure that is
stiffer in one direction than the other. .In this case the structure acts like
a spring in series with the tire but with asymmetric force-deflection proper-
ties. The resulting force-deflection loop will have a dog leg at the origin.
Although the undesirable characteristics of a fore-aft test might be obvious
when one looks at the resulting force-deflection loop, these characteristics
might go unnoticed in half cycle or increment loading tests or at least go un-
noticed until the data are plotted after the test. The simultaneous x-y re-
cording of the force and the deflection during the actual test can indicate
•
test difficulties immediately and obviously, especially when continuous load-
ing, full loops are generated. 26
Lateral Stiffness
The testing apparatus used to obtain lateral stiffness data for the model
and full size tires was the same as that used in obtaining the fore-aft data.
The only change in the model and full size equipment was to position the tire
holding yoke such that the tire was 90° from its orientation used in the fore-
aft test. Figures 11 and 12 show the model and full size lateral testing appa-
ratus. This arrangement provided a lateral force and deflection on the tire
as load was applied through the screw mechanisms of each apparatus. The forces
and deflections were measured in the same manner as in the fore-aft tests. The
same eight test techniques described for the fore-aft tests were used for the
lateral tests. The same tires and operating conditions listed in Table II were
also used, except for the standard lateral force magnitudes F . which are alsoym'
listed in Table II.
The results of the various lateral tests are summarized in Table IV.
Again, friction forces of the testing apparatus have not been taken into ac-
count for these values. Several observations can be made from these results:
(a) The values of lateral stiffness k determined from increment load«y
tests were 5-15$> less than those determined by continuous load tests. See the
results of Tests 1-5. This result was very similar to that observed for fore-
aft tests,
(b) The values of k for the model tires determined from full cycle in-«y
crement load data were 6-lC% greater than those determined from half cycle data.
This result is in direct contrast to that observed for the fore-aft tests.
27
Figure 11. Photograph of lateral test apparatus for model tires.
Figure 12. Photograph of lateral test apparatus for full size tires.
28
CO
s
H
CO
|. _ .
M < c:i-H -H
kj 0 ,0
§ H dH 15 .*»
CO
O
CO
CO
-
VO
^
-
Bo
nd
ed
b °
o
Cle
an
Meta
l' H
igh
Friction
cu•H
>
OO 4-H
^ oa; cuO 3
O nj
+1
^1
^
'
OJ
H
j-
^
II
-P /w /0 / COEH / <U
./ -H
i O i lA i 1i ON i OJ I i1 1 H 1 1
i 1 1 \D i 1I 1 I H I 11 I 1 H 1 1
1 I 1 1 1 II I 1 1 I II I 1 1 1 I
1 O i -3- i i1 CO 1 H 1 iI 1 H 1 1
1 O I VQ 1 1I CO 1 H 1 I1 1 H I I
O ON O KN O C--1 * 1 H O 1 H O N H C OI I H I1 1 1
-fl -H ' +1
COO CO KN CO VQ CO OCO i Hi ON ON
. I H Ii - i
+1 H-l -fl H-l
CO i rH i O ONI H i HI i
+1 +1 +1 +1
J lA -3- ON - 3 - C O - 3 - C OCO 1 HI O ON
1 H I H
+1 " -H +1 +1
OJ lA O J O N O J v O O j L T NON 1 OJ 1 H O
1 H i H H
-fl H-l -H +1
1 1 ITN I 1 11 1 ON 1 1 1
lA -'l \O 1 ^ C—CO i H 1 O ON
1 H i H
LA i _3- i CM IP\CO I H I O ON
I H I H
J- 1 O 1 H KNCO 1 H 1 O ON
i H 1 H
O i \o i i ONCO 1 O i 1 CO
1 H I 1
KN. i iTN i i -cf-E*- l ON l l CO
I i I
CO 1 O- f 1 VOt- i ON i i CO
i i i
PM-$ KN H (A \£) ONCVJ OJ OJ OJ OJ OJ< <C, Cp PP fp CQ
1 1 i 1 i 1 1 11 1 i 1 1 i 1 11 1 i t i i 1 1
i 1 i i 1 - i i i1 1 1 i 1 1 i ii 1 1 1 1 i i 1
1 ' i i 1 i 1 1 11 ' . i 1 1 i 1 1 11 i i 1 i 1 1 1
i i i i 1 1 i 11 i i 1 i 1 i 11 i 1 i 1 1 1 i
1 1 i 1 I I i 1
<r\o o o o o o o o oI OJvO 1 I L T N v O O t — i T N j - K N O NI CM>O I 1 O J l T N l T N O C M r — OJt--1 I I O J
+1 +1 +1 -HI +1
8 0 o o o o o o o o Q O o o o ot— OON OON uAoj OD- oo j OMD OH
OJC-- CMvo OJiTN r-{ \o OJiT\ J~H OJ{>- C X J c OOJ
H-l +1 fl +1 ' +1 -H -fl +1
o o o o o o o o o o o o o o o oITNO uNON LTNON O^O LTNO OCO lA ON ^AKNHCO H\O HLTN HM^ H\O KNH Ht>- HCO
OJ
8 O O O Q O ifNO O O O O O O O Ot- OJ- OOJ D--\£) OOJ OO OlA OON
HCO H t- HMD \o H\O o jo j HCO HCOCVJ
+1 +1 -H -fl -H +1 -fl -fl
o o o o o o o o o o o o o o o oiTv KN LTNH lAcO lA H LTNcO OON lAcO lA C—
ON cO vO Cv \ D H K N ON ONOJ
+1 -fl -fl H-l +1 H-l -H -fl
i i 1 O 1 1 I I1 1 1 KN 1 1 1 11 1 1 ITN 1 1 1 1
O O O O O O O-OCO CO ON OJ "vO J~ J OC T \ Q i A V O t A O O - C O
OJ
o o o o o o o o-3" -Q CO O LPv H J" ON
OJ
o o o o o o o oH C M ^ H K N J - O N V O
OJ
o o o o o o o oC O H \ n _ ; f O J l A c Q O
H
o o o o o o o oH - ^ - c p O O J - b - Ot * - V O l A \ O l A f — M D C —
O O O O O O O O
H
O J P T N J - i T N t — C O O N O
29
However, the full cycle values of k for the full size tires were within ±iX
of the half cycle values, as they were for the fore-aft tests. Figure 1J shows
typical increment lateral load-deflection plots for a model and a full size
tire. Again the friction force is indicated on the plot, but is not subtracted
from the data. Again it is apparent that different values of k can be deter-«y
mined with different interpretations of the data.
(c) Unlike the fore-aft results, the ratio of F /& was usually betweenym' ym
the values of k determined for Tests 1 and 2.y
(d) The values of k determined from fast increment loading loops were«y
0-11% greater than those determined from the slower increment loading loops.
Again this result agrees with the fore-aft test results.
(e) The values of k determined from fast continuous loading loops were*/
0-5$> greater than those determined from slower continuous loading loops. Again
this result agrees with the fore-aft test results.
(f) The values of k determined by measuring plate deflection and as-tX
suming it to be tire deflection were 12-17% lower than those determined by
measuring the relative displacement between plate and yoke. This result is
lower than that obtained from the fore-aft tests and might be expected. Al-
though the testing system has the same effective stiffness as before, the lat-
eral stiffness of the tire is approximately 1/5 the fore-aft stiffness. Thus,
the percentage of the total lateral deflection due to the structure is lower
than in the case of the fore-aft deflection.
(g) The values of k decreased 13-2*4% as the force loop size was in-•J
creased from a small prescribed value to a maximum size. This difference is
30
Fydbs.)
A24P0
= 20 psiFz = 41 Ibs
-2--
-4 - -
-6- -
4- H 1 h0.02 0.04 0.06 0.08 5 y ( i n . )
TIRE 87.50x 14 Typem
P0 = 87 PSi6Z =1.70 in.
Fy ( I bs )
\—h0.1 0.2 0.3 6 (in.)
Figure 1J. Typical lateral, increment load, force-deflectionplots for model and full size tires.
31
clearly seen in Figures lU and 15- Figure lU is a typical composite force-
deflection plot for two different size loops for a model tire. Figure 15 is
a similar plot for a full size tire. A dimensionless plot of lateral stiff-
ness versus lateral loop size for all the Test 7 results is shown in Figure 16.
(h) For the model tires, the value of k varied less than 2tf0 for the dif-«y
ferent surface conditions tested and increased 9~H$> when bonded to the surface.
A comparison of the lateral stiffness results with the fore-aft stiffness
results indicates that, generally, the effects of testing techniques on these
two mechanical properties are similar in nature, although the degree of influ-
ence on fore-aft properties appear to be greater. Thus, the observations and
recommendations made for fore-aft stiffness can also be made for lateral stiff-
ness.
Vertical Stiffness
The test apparatus used to obtain vertical stiffness data for the model
tires is shown in Figure 17. This apparatus is yet another adaptation of the
Static Testing Device described in [1]. In its use as a vertical stiffness
test stand, the wheel and yoke were rigidly blocked up off the movable bearing
plate. A "vertical" load was then applied horizontally to the tire by loading
a rigid vertical surface against the tire. The vertical wall was attached to
the bearing plate and the load was applied'through the screw mechanism. The
resulting "vertical" deflection was measured by the LVDT mounted between the
bearing plate and the yoke. The force was measured with the same force
32
B291
P0 = 25 Psi
Fz =31.6lbs
Fy (Ibs)
-0.075 0.025 0.050 0.075 6 (in.)
Figure 1 4-. Lateral force-deflection loops illustratingeffect of loop size for a model tire.
33
TIRE 8
7.50x14 TypemP0
= 87 psi
6z=1.70in.
F y ( lbs)
500 --
FrictionForce
4-
250 --Fy ^ 500
-0.250 -0.125 0.125
Fy ^ ± 200
0.250 6y( in.)
-500 --
Figure 15. Lateral force-deflection loops illustratingeffect of loop size for a full size tire.
34
_POD
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
00 0.01 0.02 0.03
/p0D20.04 0.05
Figure l6. Dimensionless plot of lateral stiffnessversus loop size for all tires.
35
Figure 17• Photograph of vertical test apparatus for model tires.
transducer used for the previous tests. Again the output signals of the trans-
ducers were amplified and recorded on an x-y plotter.
The Riehle test machine used to obtain vertical stiffness for the full
size tires was basically that illustrated in Figure J. In this test the ver-
tical load was applied through the movable loading head of the test machine
and the resulting vertical deflection measured with a dial gage. For the ver-
tical tests, four testing techniques were used to obtain vertical stiffness
data. These techniques are described below as Tests A, B, C, and D.
Test A - Increment deflections.
The tire was inflated to the value listed in Table II. An increment of
vertical deflection was applied and held constant for one minute at which time
the vertical load was recorded. An identical increment of deflection was then
applied and the procedure repeated. This test procedure was continued until
36
the maximum desired deflection was obtained. The increment deflections were
then decreased to zero. The value of the vertical stiffness k was then deter-z
mined by measuring the slope of the line joining the maximum end point of the
force-deflection loop and the point whose coordinates were one half the maximum
deflection and the average force of the increasing and decreasing portions of
the loop at this deflection.
Test B - Continuous slow loop.
This test was a repeat of Test A except the vertical deflection was ap-
plied in a continuous manner. The time for one complete cycle was at least
one minute.
Test C - Continuous fast loop.
This test was a repeat of Test B except the loop was complete in approxi-
mately 15 seconds.
Test D - Looping about a predeflection.
The tire was inflated to the specified value in Table II and deflected to
one half of its maximum vertical deflection 6 . This deflection was taken aszm
the center of a force-deflection loop. The loop was obtained by starting at
this point as zero reference and slowly and continuously applying an increasing
vertical deflection to a value short of 5 and then decreasing the deflectionzm
back through the reference point towards the real zero deflection, but re-
versing the deflection before zero was reached and increasing the deflection
to the reference point. The value of k was then determined by measuring thez
slope of the line joining the end points of the loop.
A summary of the results from these four tests is shown in Table V. Again
37
TABLE V
SUMMARY OF STATIC VERTICAL STIFFNESS
k (Ib/in. )z
Tires
A2UB21B26B291
12
3l*5678910
TestFzm°zm
lUO170180180
2630100010308107506108 0306012101380
A
kz
160220230230
32601210120090081*0690950
1*070ll*7011*10
TestFzmzm
11*0170180
" 190
2660103010508107606108503090122011*00
B
kz
1602202302UO
326012901260900876700980
1*120150011*6 o
TestFZm5zm
11*0170180190
2650ioi*o10608207806208603130121*011*20
C
kz
1602202302UO
321*0130012609209007209703980-157011*60
TestFzm6
150180190 '200
289011801130850850660920
• 31*2013201550
D
kz
160210220230
329013201290920880700990
l*ll*01580ll*90
some general observations can be made. First, in general, the variation of
the values of! k from Test A through Test D was less than 5/0- Secondly, inZ
general, the ratio of the maximum load to the maximum deflection, F /& , waszm' zm
appreciably less (5-20/J than the value of k . See the results of Tests A, B,Z
and C. This result is clearly indicated in Figures 18 and 19, which show typ-
ical vertical force-deflection curves for the model and full size tires, re-
spectively. In these figures a definite nonlinearity is evident in the lower
portion of the curve. This nonlinearity diminishes as the contact patch be-
comes fully developed under, the influence of the vertical deflection. Thus,
the ratio of F /& was less than k because the F was proportionatelyzm zm z z
smaller for the first half of the loop than'for the second half.
38
40
35
30
25
20
(Ibs.)
15
10
0
B291
= 25psi
0 0.05
Looping aroundfixed deflection
I0.10 0.15
6z( in.)0.20
Figure 18- Typical vertical force-deflection loop for a model tire.
39
' z(Ibs)
5000 r-
4500 k
4000k
3500 k
3000k
2500k
2000 k
1500k
1000 k
500 k
TIRE 12 4 x 7 . 7 - 10PR Type YEP0 = 85 psi
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
62 (In.)
Figure 19. Typical vertical force-deflection loop for a full size tire.
40
Finally, the value of k was not appreciably changed when determined fromz
the slope of the line through the end points of the loop generated by cycling
about 6 /2. This result is obvious after observing a typical loop and itszm
corresponding full loop shown in Figure-18. It is evident in this figure that
looping about a predeflection point does not effect the value of k as long asz
the loop does not extend significantly into the lower nonlinear region.
From these observations it might be recommended that the most consistent
way to evaluate k is to establish a definition which will eliminate the ini-z
tial "soft" portion of the vertical load-deflection curve, such as the defini-
tion of k used in this study. The technique used to obtain the force-z
deflection information seems to make little or no different in the value for
k .z
41
CONCLUDING REMARKS
Fore-aft, lateral, and vertical spring rates of model and full-scale
pneumatic tires were evaluated by testing techniques generally employed
by industry and various testing groups. The purpose of this experimental
program was to investigate what effects the different testing techniques
have on the measured values of these important static tire mechanical
properties. Of the three properties evaluated, the fore-aft stiffness
was demonstrated to be the most affected by the different testing techniques
used to obtain it. Appreciable differences in the fore-aft spring rates
occurred using both the increment- and continuous-loading techniques; how-
ever, the most significant effect was attributed to variations in the size
of the fore-aft force loop. The techniques which provided the most con-
sistent value in fore-aft stiffness was that of generating and recording a
continuous full-cycle force-deflection loop.
The dependence of lateral stiffness values on testing techniques
followed the same trends as fore-aft stiffness values, except to a lesser
degree. Vertical stiffness values were found to be nearly independent of
testing procedures and techniques; however, due to a characteristic initial
"soft" portion in the vertical load-deflection curve, consistent values of
vertical stiffness can only be obtained when its value is determined from
a definition that bypasses the initial nonlinear portion of the force-
deflection curve.
The research program described in this paper indicates that testing
techniques do have an effect on the measured values of the three static
42
stiffnesses studied. As more tire user groups demand to know more tire
characteristics, the need for a uniform criteria to measure and interpret
values for these tire characteristics grows and it is hoped that this
study might be used as a preliminary indication of how such a criteria
may "be formulated. Eventually, slow rolling properties such as cornering
power, self-aligning torque, pneumatic trail, and relaxation length must
also be exhaustively studied if the values of these tire parameters are
to have meaning to the tire user group. However, the basic static tire
properties covered in this report are probably the most amenable to some
sort of measurement and interpretation standard. The results given in
this report do serve to provide some indication of the type of measurement
and the difficulties of measurement interpretation that must be thoroughly
investigated before such a standard can be proposed.
43
REFERENCE
[1] Clark, S. K., Dodge, R. N., Lackey, J. I., and Nybakken, G. H., "Struc-tual Modeling of Aircraft Tires," NASA CR-2220, National Aeronauticsand Space Administration, Washington, D. C., 1973-
44 NASA-Langley, 1974 CR-2U12
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
WASHINGTON. D.C. 2O546
OFFICIAL BUSINESS
SPECIAL FOURTH-CLASS RATEBOOK
POSTAGE AND FEES PAID
NATIONAL AERONAUTICS ANDSPACE ADMINISTRATION
451
POSTMASTER : If Undeliverable (Section 158Postal Manual) Do Not Return
"The aeronautical and space activities of the United States shall beconducted so as to contribute . . . to the expansion of human knowl-edge of phenomena in the atmosphere and space. The Administrationshall provide for the widest practicable and appropriate disseminationof information concerning its activities and the results thereof."
—NATIONAL AERONAUTICS AND SPACE ACT OF 1958
NASA SCIENTIFIC AND TECHNICAL PUBLICATIONSTECHNICAL REPORTS: Scientific andtechnical information considered important,complete, and a lasting contribution to existingknowledge.
TECHNICAL NOTES: Information less broadin scope but nevertheless of importance as acontribution to existing knowledge.
TECHNICAL MEMORANDUMS:Information receiving limited distributionbecause of preliminary data, security classifica-tion, or other reasons. Also includes conferenceproceedings with either limited or unlimiteddistribution.
CONTRACTOR REPORTS: Scientific andtechnical information generated under a NASAcontract or grant and considered an importantcontribution to existing knowledge.
TECHNICAL TRANSLATIONS: Informationpublished in a foreign language consideredto merit NASA distribution in English.
SPECIAL PUBLICATIONS: Informationderived from or of value to NASA activities.Publications include final reports of majorprojects, monographs, data compilations,handbooks, sourcebooks, and specialbibliographies.
TECHNOLOGY UTILIZATIONPUBLICATIONS: Information on technologyused by NASA that may be of particularinterest in commercial and other non-aerospaceapplications. Publications include Tech Briefs,Technology Utilization Reports andTechnology Surveys.
Details on the availability of these publications may be obtained from:
SCIENTIFIC AND TECHNICAL INFORMATION OFFICE
N A T I O N A L A E R O N A U T I C S A N D S P A C E A D M I N I S T R A T I O NWashington, D.C. 20546
